When using the astrophysically motivated prior for \(m_\mathrm {max}\) , the posterior closely follows the prior.
The posterior on \(m_\mathrm {max}\)  is more restricted at smaller values of the power-law index \(\alpha \) : when the mass distribution is flatter we are more sensitive to the upper cutoff than when the distribution sharply decreases with mass and we can increase the upper cutoff with little consequence [1]}.
When switching to the uniform prior on \(m_\mathrm {max}\)  we see the same qualitative behavior with varying \(\alpha \) .
For steep power laws (\(\alpha \gtrsim 2\) ), we are effectively insensitive to the existence of an upper cutoff, but for flatter power laws (\(\alpha \lesssim 1\) ), the dearth of higher-mass black holes means that there is little posterior support for \(m_\mathrm {max} \gtrsim 45 M_\odot \) .
